We present STARFlow, a scalable generative model based on normalizing flows that achieves strong performance in high-resolution image synthesis. The core of STARFlow is Transformer Autoregressive Flow (TARFlow), which combines the expressive power of normalizing flows with the structured modeling capabilities of Autoregressive Transformers. We first establish the theoretical universality of TARFlow for modeling continuous distributions. Building on this foundation, we introduce several key architectural and algorithmic innovations to significantly enhance scalability: (1) a deep-shallow design, wherein a deep Transformer block captures most of the model representational capacity, complemented by a few shallow Transformer blocks that are computationally efficient yet substantially beneficial; (2) modeling in the latent space of pretrained autoencoders, which proves more effective than direct pixel-level modeling; and (3) a novel guidance algorithm that significantly boosts sample quality. Crucially, our model remains an end-to-end normalizing flow, enabling exact maximum likelihood training in continuous spaces without discretization. STARFlow achieves competitive performance in both class-conditional and text-conditional image generation tasks, approaching state-of-the-art diffusion models in sample quality. To our knowledge, this work is the first successful demonstration of normalizing flows operating effectively at this scale and resolution.

Soil moisture is one of the primary hydrological state (memory) variables in terrestrial systems (Dobriyal et al. 2012; Rossato et al. 2017a), and is one of the primary controls for agriculture and water management (Dobriyal et al. 2012; Rossato et al. 2017b). Soil moisture affects evapotranspiration and vegetation water availability, which are at the core of the climate-carbon cycle (Falloon et al. 2011) and play an important role in hydrological risks such as floods, drought, erosion, and landslides (Kim et al. 2019; Legates et al. 2011; Tramblay et al. 2012). Accurate measurement of soil moisture has numerous downstream benefits (Moran et al. 2015) including reduced water wastage by better understanding and managing the consumption of water (Brocca et al. 2018; Foster, Mieno, and Brozović 2020), utilising smarter irrigation methods (Kumar et al. 2014) and effective canal water management (Zafar, Prathapar, and Bastiaanssen 2021). The most accurate way to measure soil moisture is via ground-based methods such as direct gravimetric measurements (Klute 1986) or indirect methods such as dielectric reflectometry, capacitance charge, etc. (Bittelli 2011), which in-situ sensors utilize (Walker, Willgoose, and Kalma 2004). However, in-situ sensors are difficult to scale spatially, and are expensive to install and maintain.

The most common representation formalisms for automated planning are descriptive models that abstractly describe what the actions do and are tailored for effciently computing the next state(s) in a state-transition system. However, real-world acting requires operational models that describe how to do things, with rich control structures for closed-loop online decision-making in a dynamic environment. To use a different action model for planning than the one used for acting causes problems with combining acting and planning, in particular for the development and consistency verification of the different models. As an alternative, we define and implement an integrated acting-and-planning system in which both planning and acting use the same operational models, which are written in a general-purpose hierarchical task-oriented language offering rich control structures. The acting component, called Reactive Acting Engine (RAE), is inspired by the well-known PRS system, except that instead of being purely reactive, it can get advice from the planner. Our planner uses a UCT-like Monte Carlo Tree Search procedure, called UPOM (UCT Procedure for Operational Models), whose rollouts are simulations of the actor's operational models. We also present learning strategies for use with RAE and UPOM that acquire, from online acting experiences and/or simulated planning results, a mapping from decision contexts to method instances as well as a heuristic function to guide UPOM. Our experimental results show that UPOM and our learning strategies significantly improve the acting efficiency and robustness of RAE. We discuss the asymptotic convergence of UPOM by mapping its search space to an MDP.